Matrix KSGNS construction and a Radon--Nikodym type theorem
Operator Algebras
2021-07-23 v3 Functional Analysis
Abstract
In this paper, we introduce the concept of completely positive matrix of linear maps on Hilbert -modules over locally -algebras and prove an analogue of Stinespring theorem for it. We show that any two minimal Stinespring representations for such matrices are unitarily equivalent. Finally, we prove an analogue of the Radon--Nikodym theorem for this type of completely positive matrices.
Cite
@article{arxiv.1608.01672,
title = {Matrix KSGNS construction and a Radon--Nikodym type theorem},
author = {M. S. Moslehian and A. Kusraev and M. Pliev},
journal= {arXiv preprint arXiv:1608.01672},
year = {2021}
}
Comments
17 pages; The paper was revised and some material is added to it. To appear in Indag. Math